{
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   "metadata": {},
   "source": [
    "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Challenge Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Find the shortest path between two nodes in a graph.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)\n",
    "* [Solution Notebook](#Solution-Notebook)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "\n",
    "* Is this a directional graph?\n",
    "    * Yes\n",
    "* Could the graph have cycles?\n",
    "    * Yes\n",
    "    * Note: If the answer were no, this would be a DAG.  \n",
    "        * DAGs can be solved with a [topological sort](http://www.geeksforgeeks.org/shortest-path-for-directed-acyclic-graphs/)\n",
    "* Are the edges weighted?\n",
    "    * Yes\n",
    "    * Note: If the edges were not weighted, we could do a BFS\n",
    "* Are the edges all non-negative numbers?\n",
    "    * Yes\n",
    "    * Note: Graphs with negative edges can be done with Bellman-Ford\n",
    "        * Graphs with negative cost cycles do not have a defined shortest path\n",
    "* Do we have to check for non-negative edges?\n",
    "    * No\n",
    "* Can we assume this is a connected graph?\n",
    "    * Yes\n",
    "* Can we assume the inputs are valid?\n",
    "    * No\n",
    "* Can we assume we already have a graph class?\n",
    "    * Yes\n",
    "* Can we assume we already have a priority queue class?\n",
    "    * Yes\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "The constraints state we don't have to check for negative edges, so we test with the general case.\n",
    "\n",
    "<pre>\n",
    "graph.add_edge('a', 'b', weight=5)\n",
    "graph.add_edge('a', 'c', weight=3)\n",
    "graph.add_edge('a', 'e', weight=2)\n",
    "graph.add_edge('b', 'd', weight=2)\n",
    "graph.add_edge('c', 'b', weight=1)\n",
    "graph.add_edge('c', 'd', weight=1)\n",
    "graph.add_edge('d', 'a', weight=1)\n",
    "graph.add_edge('d', 'g', weight=2)\n",
    "graph.add_edge('d', 'h', weight=1)\n",
    "graph.add_edge('e', 'a', weight=1)\n",
    "graph.add_edge('e', 'h', weight=4)\n",
    "graph.add_edge('e', 'i', weight=7)\n",
    "graph.add_edge('f', 'b', weight=3)\n",
    "graph.add_edge('f', 'g', weight=1)\n",
    "graph.add_edge('g', 'c', weight=3)\n",
    "graph.add_edge('g', 'i', weight=2)\n",
    "graph.add_edge('h', 'c', weight=2)\n",
    "graph.add_edge('h', 'f', weight=2)\n",
    "graph.add_edge('h', 'g', weight=2)\n",
    "shortest_path = ShortestPath(graph)\n",
    "result = shortest_path.find_shortest_path('a', 'i')\n",
    "self.assertEqual(result, ['a', 'c', 'd', 'g', 'i'])\n",
    "self.assertEqual(shortest_path.path_weight['i'], 8)\n",
    "</pre>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "Refer to the [Solution Notebook](http://nbviewer.jupyter.org/github/donnemartin/interactive-coding-challenges/blob/master/graphs_trees/graph_shortest_path/graph_shortest_path_solution.ipynb).  If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%run ../../arrays_strings/priority_queue/priority_queue.py\n",
    "%load ../../arrays_strings/priority_queue/priority_queue.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%run ../graph/graph.py\n",
    "%load ../graph/graph.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "class ShortestPath(object):\n",
    "\n",
    "    def __init__(self, graph):\n",
    "        # TODO: Implement me\n",
    "        pass\n",
    "\n",
    "    def find_shortest_path(self, start_node_key, end_node_key):\n",
    "        # TODO: Implement me\n",
    "        pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**The following unit test is expected to fail until you solve the challenge.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# %load test_shortest_path.py\n",
    "import unittest\n",
    "\n",
    "\n",
    "class TestShortestPath(unittest.TestCase):\n",
    "\n",
    "    def test_shortest_path(self):\n",
    "        graph = Graph()\n",
    "        graph.add_edge('a', 'b', weight=5)\n",
    "        graph.add_edge('a', 'c', weight=3)\n",
    "        graph.add_edge('a', 'e', weight=2)\n",
    "        graph.add_edge('b', 'd', weight=2)\n",
    "        graph.add_edge('c', 'b', weight=1)\n",
    "        graph.add_edge('c', 'd', weight=1)\n",
    "        graph.add_edge('d', 'a', weight=1)\n",
    "        graph.add_edge('d', 'g', weight=2)\n",
    "        graph.add_edge('d', 'h', weight=1)\n",
    "        graph.add_edge('e', 'a', weight=1)\n",
    "        graph.add_edge('e', 'h', weight=4)\n",
    "        graph.add_edge('e', 'i', weight=7)\n",
    "        graph.add_edge('f', 'b', weight=3)\n",
    "        graph.add_edge('f', 'g', weight=1)\n",
    "        graph.add_edge('g', 'c', weight=3)\n",
    "        graph.add_edge('g', 'i', weight=2)\n",
    "        graph.add_edge('h', 'c', weight=2)\n",
    "        graph.add_edge('h', 'f', weight=2)\n",
    "        graph.add_edge('h', 'g', weight=2)\n",
    "        shortest_path = ShortestPath(graph)\n",
    "        result = shortest_path.find_shortest_path('a', 'i')\n",
    "        self.assertEqual(result, ['a', 'c', 'd', 'g', 'i'])\n",
    "        self.assertEqual(shortest_path.path_weight['i'], 8)\n",
    "\n",
    "        print('Success: test_shortest_path')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestShortestPath()\n",
    "    test.test_shortest_path()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Solution Notebook\n",
    "\n",
    "Review the [Solution Notebook](https://github.com/donnemartin/interactive-coding-challenges/graphs_trees/graph_shortest_path/graph_shortest_path_solution.ipynb) for a discussion on algorithms and code solutions."
   ]
  }
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